It is likely that the origin of this family name can be found in the following factors: CODA, which means "tail" or "queue", is the Italian equivalent of the Latin CAUDA, and both are surnames currently used in Italy.
In this case both CODA and CAUDA find their roots in the name of the SAMNITE city of CAUDIO, approximately thirty miles East of Naples.
According to history, in one of the shrewdest battles, Rome was defeated and made to kneel under the "Caudium forculae".In the aftermath the younger "Caudini" spread around as praised mercenaries.
The name in Irish is Mac ODA, and was derived from Odo le Ercedekne, whose family had settled in County Kilkenny at the beginning of the 13th century.
The Irish Coda (Cody) settlers came, evidently, from the South of England (Cornwall) where the Norman invaders had already moved (William the Conqueror and Domesday in 1066) with the consent of the Church of Rome who financed the operation and provided "Samnite mercenaries" from the Caudium area.